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Members of the general adult population volunteer an average of 4.2 hours per we

ID: 2958748 • Letter: M

Question

Members of the general adult population volunteer an average of 4.2 hours per week. A random sample of 20 female college students and 18 male college students produced the results given in the table below. At the .01 level of significance, is there sufficient evidence to conclude that a difference exists between the mean number of volunteer hours per week for male and female college students?

Females Males
Sample size 20 18
Sample mean 3.8 2.5
Sample variance 3.5 2.2

A. No, because the test value 2.38 is greater than the critical value
B. No, because the test value 2.38 does not exceed the critical value
C. No, because the test value 2.90 is greater than the critical value
D. Yes, because the test value 2.90 is greater than the critical value

Explanation / Answer

The test hypothesis is
Ho:1=2
Ha:1 not equal to 2

The test statisitc is

t=(xbar1-xbar2)/[s1^2/n1+s2^2/n2]

=(3.8-2.5)/sqrt(3.5/20+2.2/18)

=2.38


Given a=0.01, the critical value is |t(0.005, df=n1+n2-2=36)|=2.72 (check student t table)

Since 2.38 is less than 2.72, we do not reject Ho.

Answer:B. No, because the test value 2.38 does not exceed the critical value